GCSE Maths • Foundation & Higher
GCSE Standard Form Revision Guide
Write, compare and calculate with very large and very small numbers.
Foundation
Exam practice
Worked examples
What You'll Learn
Recognise Valid Standard Form
Check the coefficient range and integer exponent.
Convert into Standard Form
Place the decimal correctly and choose the matching power of 10.
Convert to Ordinary Numbers
Use the exponent to restore place value and zeros.
Multiply and Divide
Apply index laws, then renormalise the coefficient.
Add and Subtract
Rewrite with a common power before combining coefficients.
Use Calculator Notation
Enter and interpret EXP, EE or ×10ˣ notation accurately.
Key Rules and Formulas
Scatter Graphs Lessons
Calculations With Standard Form
Use index laws and coefficient calculations, then return answers to valid standard form.
Converting Standard Form
Convert large and small numbers into standard form and back into ordinary notation.
CORE SUBTOPICS
Place Value and Zeroes
Track the decimal point without losing internal or trailing zeroes.
Negative Indices
Interpret 10⁻ⁿ as 1/10ⁿ.
Normalising Coefficients
Convert forms such as 24 × 10⁵ into 2.4 × 10⁶.
Significant Figures
Round the coefficient to the requested accuracy without changing the power incorrectly.
Order of Magnitude
Use exponents to compare scale and estimate sensible answers.
Science Applications
Apply units consistently to distances, masses, populations and microscopic quantities.
Worked Example
Adding Numbers with Different Powers
QUESTION
Calculate (3.6 × 10⁵) + (4.8 × 10⁴). Give the answer in standard form.
- Given information: The powers must match before the coefficients can be added.
- Method: Rewrite the smaller term using 10⁵, add the coefficients, then check the coefficient range.
- Rewrite 4.8 × 10⁴ as 0.48 × 10⁵.
- Keep the common power: 4.08 × 10⁵.
- The coefficient 4.08 is at least 1 and less than 10, so no further renormalisation is needed.
- Final answer: 4.08 × 10⁵.
- Independent answer check: 360,000 + 48,000 = 408,000 = 4.08 × 10⁵.
- One common mistake: Do not calculate 3.6 + 4.8 while leaving different powers of ten unchanged.
- Common GCSE Mistakes
- Invalid Coefficient
- Wrong Exponent Sign
- Counting Zeroes Instead of Places
- Forgetting to Renormalise
- Adding Different Powers Directly
- Using the Wrong Index Law
- Incorrect Calculator Entry
- Rounding Too Early
- Exam Tips
- Write the coefficient condition beside your first conversion practice.
- Use the original number’s size to sense-check the exponent sign.
- After multiplying or dividing, renormalise before giving the final answer.
- For addition or subtraction, rewrite using a common exponent first.
- Keep units attached and convert units before calculating when required.
- Estimate the exponent before using a calculator.
- Learn how your calculator displays and enters scientific notation.
Ready to Practice?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Standard Form Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
It writes a non-zero number as a × 10ⁿ with an integer n and a coefficient of valid size.
For positive numbers, 1 ≤ a < 10. For signed numbers, the equivalent condition is 1 ≤ |a| < 10.
Because 10⁻ⁿ = 1/10ⁿ, so it scales the coefficient down.
Multiply coefficients, add exponents and renormalise.
It is calculator notation for 5.2 × 10⁷.
Latest Standard Form Guides
Revision Resource In Your Inbox
Get expert revision tips, study resources, and exam support delivered straight to your inbox.
